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The purpose of this article is to propose a modified hybrid projection algorithm and prove a strong convergence theorem for closed and quasi-strict pseudo-contractions. Its results hold in reflexive, strictly convex and smooth Banach spaces with the property (K). The results of this paper improve and extend the corresponding results of Matsushita and Takahashi (J. Approx. Theory 134:257–266, ), Qin and Su (Nonlinear Anal. 67:1958–1965, ), Marino and Xu (J. Math. Anal. Appl. 329:336–346, ) and others. [ABSTRACT FROM AUTHOR]

The purpose of this article is to propose a modified hybrid projection algorithm and prove strong convergence theorems for a family of quasi- φ-asymptotically nonexpansive mappings. The results of this paper improve and extend the results of S. Matsushita and W. Takahashi (J. Approx. Theory, 134: 257–266 (2005)), T.H. Kim, H.K. Xu (Nonlinear Anal. 64: 1140–1152 (2006)), Y.F. Su, D.X. Wang, M.J. Shang (Fixed Point Theory Appl. 2008: 284613 (2008)) and others. [ABSTRACT FROM AUTHOR]

In this paper internal characterization on certain quotient images of locally separable metric spaces are discussed. We obtain some descriptions of quotient s-images, pseudo-open s-images, quotient compact images and closed images of locally separable metric spaces, and establish some relations between these and certain quotient images of metric spaces by the local separability of suitable subspaces. [ABSTRACT FROM AUTHOR]

Some properties generalizing the normality separation axiom and their behavior under basic topological operations and continuous mappings are discussed. One of the general problems considered in the paper concerns the deduction of “nice” topological properties of spaces from generalized normality of certain topological products, their subspaces, and other related structures; in particular, extensions of the well-known theorems of Katetov and Tamano are suggested. [ABSTRACT FROM AUTHOR]

We establish relationships between paracompact locally Lindelöf spaces and all kinds of spaces with L-systems by means of closed mappings, weakly perfect mappings and quotient mappings. In particular, we obtain some characterizations of paracompact locally Lindelöf spaces. Interestingly, they are also characterized as weakly perfect inverse images of locally separable metric spaces. [ABSTRACT FROM AUTHOR]